At , a differentiable function satisfies . It is known that for all . Identify the…

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

x = 3

, a differentiable function

f

satisfies

f'(3)=0

. It is known that

f'(x)>0

for all

x<3

and

f'(x)<0

for all

x>3

. Identify the nature of the point

x=3

on the graph of

f

and state the reason for your answer.